Cauchy–Davenport Sprint

Cauchy–Davenport Sprint

Build sets A and B in ℤ/pℤ, watch their sumset size vs. the lower bound.

A

B

A+B

Prime p

Tip: equality often occurs when A and B are intervals (or near-intervals).

|A|

0

|B|

0

|A+B|

0

Lower bound

0

Gap = |A+B| − min(p, |A|+|B|−1)

0

Try forming intervals to hit the bound.

Cauchy–Davenport inequality (one-paragraph brief)

For nonempty subsets A, B of the finite cyclic group ℤ/pℤ with p prime, the Cauchy–Davenport inequality states |A + B| ≥ min(p, |A| + |B| − 1), where A + B = { a + b (mod p) : a ∈ A, b ∈ B }. In many near‑extremal cases, A and B look like intervals (arithmetic progressions) modulo p. This game lets you experiment by toggling elements on a circle for ℤ/pℤ and comparing the sumset size with the lower bound.

Controls: Click points to toggle membership in the active set (Edit set A / Edit set B). Use “Make into an interval” to test near‑equality patterns. “Randomize” gives quick starting points.